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A certain store sells only black shoes and brown shoes. In a certain

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New post 25 Nov 2011, 13:55
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A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/3 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?

A. x/3
B. x/2
C. 2x/3
D. 3x/2
E. 2x
[Reveal] Spoiler: OA

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Last edited by Bunuel on 24 Dec 2014, 03:24, edited 1 time in total.
Renamed the topic and edited the question.
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New post 25 Nov 2011, 14:31
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x/(x+y) = 2/3
3x = 2x+2y
x = 2y
y = x/2

B
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New post 24 Dec 2014, 03:20
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Assume the store sold 30 shoes.

Black shoes=20 and Brown=10.
So brown shoes are half(1\2) of black shoes.
Ans B.
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New post 30 Dec 2014, 23:20
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Total shoes sold = x+y

Given that \(\frac{2}{3} rd\) of total shoes sold are black

\(\frac{2}{3} (x+y) = x\)

\(y = \frac{x}{2}\)

Answer = B
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New post 03 Jan 2015, 04:05
I also used the same approach as PareshGmat, but I would like to post a more detailed solution:

Let's say that x is the number of black shoes sold and y the number of brown shoes sold.
Then, x+y is the total number of shoes that were sold. [1]
2/3 of the total shoed sold (x+y) were black (x): this translates in 2/3 of x+y, which is 2/3*(x+y).

Then, [1] becomes:
x+y= 2/3(x+y) + y
x+y - 2/3(x+y) = y
x+y - (2x+2y)/3 = y
[3(x+y)-2x+2y]/3 = y
(3x+3y-2x+2y)/3= y
(x+y)/3=y
x+y = 3y
x= 2y
y=x/2 B
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Re: A certain store sells only black shoes and brown shoes. In a certain   [#permalink] 08 Mar 2016, 02:16
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